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Question


How many pairs of co-prime natural numbers a and b exist such that a + b = 510?


Options:
A .   60
B .   120
C .   64
D .   128
Answer: Option C
:
C

510=2×3×5×17.
Use the concept of Euler's theorem:
510(112)(113)(115)(1117)=128
Number of pairs=1282=64.



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